Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete, 2006
Proceedings of the NATO Advanced Research Workshop on Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete St. Petersburg, Russia, 15-19 September 2002
NATO Science Series II: Mathematics, Physics and Chemistry Series, Vol. 201

THE CKP HIERARCHY AND THE WDVV PREPOTENTIAL.- QUANTUM INVARIANCE GROUPS OF PARTICLE ALGEBRAS.- ALGEBRAIC HIROTA MAPS.- BOUNDARY STATES IN SUSY SINE-GORDON MODEL.- GEOMETRY OF DISCRETE INTEGRABILITY. THE CONSISTENCY APPROACH.- HOMOCLINIC ORBITS AND DRESSING METHOD.- RIEMANN-HILBERT PROBLEM AND ALGEBRAIC CURVES.- ANALYTIC AND ALGEBRAIC ASPECTS OF TODA FIELD THEORIES AND THEIR REAL HAMILTONIAN FORMS.- BILINEAR AVATARS OF THE DISCRETE PAINLEV II EQUATION.- ORTHOGONAL POLYNOMIALS SATISFYING Q-DIFFERENCE EQUATIONS.- DISCRETIZATION OF COUPLED SOLITON EQUATIONS.- AN ADELIC W-ALGEBRA AND RANK ONE BISPECTRAL OPERATORS.- TOROIDAL LIE ALGEBRA AND BILINEAR IDENTITY OF THE SELF-DUAL YANG-MILLS HIERARCHY.- FROM SOLITON EQUATIONS TO THEIR ZERO CURVATURE FORMULATION.- COVARIANT FORMS OF LAX ONE-FIELD OPERATORS: FROM ABELIAN TO NONCOMMUTATIVE.- ON THE DIRICHLET BOUNDARY PROBLEM AND HIROTA EQUATIONS.- FUNCTIONAL-DIFFERENCE DEFORMATIONS OF DARBOUX-P ÖSHL-TELLER POTENTIALS.- MAXWELL EQUATIONS FOR QUANTUM SPACE-TIME.- A SOLVABLE MODEL OF INTERACTING PHOTONS.- DISCRETIZATION OF A SINE-GORDON TYPE EQUATION.- HIERARCHY OF QUANTUM EXPLICITLY SOLVABLE AND INTEGRABLE MODELS.- A TWO-PARAMETER ELLIPTIC EXTENSION OF THE LATTICE KdV SYSTEM.- TRAVELLINGWAVES IN A PERTURBED DISCRETE SINE-GORDON EQUATION.- QUANTUM VS CLASSICAL CALOGERO–MOSER SYSTEMS.- GEOMETRICAL DYNAMICS OF AN INTEGRABLE PIECEWISE-LINEAR MAPPING.- FREE BOSONS AND DISPERSIONLESS LIMIT OF HIROTA TAU-FUNCTION.- SIMILARITY REDUCTIONS OF HIROTA BILINEAR EQUATIONS AND PAINLEVÉ EQUATIONS.- ON FUNDAMENTAL CYCLE OF PERIODIC BOX-BALL SYSTEMS.- COMBINATORICS AND INTEGRABLE GEOMETRY.- ON REDUCTIONS OF SOME KdV-TYPE SYSTEMS AND THEIR LINK TO THE QUARTIC HÉNON-HEILES HAMILTONIAN.- ON THE BILINEAR FORMS OF PAINLEVé'S 4TH EQUATION.